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A New Tentacles-based Technique for Avoiding
Obstacles during Visual Navigation
Andrea Cherubini, Fabien Spindler, François Chaumette
To cite this version:
Andrea Cherubini, Fabien Spindler, François Chaumette. A New Tentacles-based Technique for
Avoid-ing Obstacles durAvoid-ing Visual Navigation. ICRA: International Conference on Robotics and Automation,
May 2012, St. Paul, Minnesota, United States. pp.4850-4855. �hal-00750586�
A New Tentacles-based Technique
for Avoiding Obstacles during Visual Navigation
Andrea Cherubini, Fabien Spindler and Franc¸ois Chaumette
Abstract— In this paper, we design and validate a new tentacle-based approach, for avoiding obstacles during appearance-based navigation with a wheeled mobile robot. In the past, we have developed a framework for safe visual navigation. The robot follows a path represented as a set of key images, and during obstacle circumnavigation, the on-board camera is actuated to maintain scene visibility. In those works, the model used for obstacle avoidance was obtained using a potential vector field. Here, a more sophisticated and efficient method, that exploits the robot kinematic model, and predicts collision at look-ahead distances, is designed and integrated in that framework. Outdoor experiments comparing the two models show that the new approach presents many advantages. Higher speeds and precision can be attained, very cluttered scenarios involving large obstacles can be successfully dealt with, and the control inputs are smoother.
Index Terms— Visual Navigation, Visual Servoing, Collision Avoidance.
I. INTRODUCTION
One of the main objectives of robotics research is the development of vehicles capable of autonomously navigating in unknown environments [1], [2]. In this field, an important task is obstacle avoidance: if possible, a collision-free trajec-tory to the goal should be generated; otherwise, the vehicle must brake to prevent collision [3].
The task that we focus on is outdoor visual navigation: a wheeled vehicle, equipped with an actuated pinhole camera and with a forward-looking range scanner, must follow a path represented by key images, without colliding with the ground obstacles. The camera detects the features required for navigating, while the scanner senses the obstacles (in contrast with other works, such as [4], only one sensor is used to detect the obstacles). In the past, obstacle avoidance has been integrated in visual navigation [5], [6] and path following [7], [8], by using the path geometry or the envi-ronment 3D model (including, for example, walls and doors). However, since our task is defined in the image space, we seek a merely sensor-based solution, which does not need a global model of the environment and trajectory.
In our recent work [9] we adopted a method based on potential fields [10] built on an occupancy grid. This method, however, suffered from its simplicity, which led to very con-servative collision avoidance, and strongly varying control inputs. Alternative reactive strategies include: the vector field histogram [11], dynamic window [12], obstacle-restriction method [13], and closest gap [14]. The first two methods rely on a candidate set of commands; however, trap situations and oscillations may arise. In [13], these issues are solved, but, since the robot is assumed holonomic and a 3D subgoal
A. Cherubini was with INRIA Rennes - Bretagne Atlantique, IRISA, Campus de Beaulieu 35042, Rennes, France, and is now with the Laboratory for Computer Science, Microelectronics and Robotics LIRMM - Univer-sit´e de Montpellier 2 CNRS, 161 Rue Ada, 34392 Montpellier, France. {Andrea.Cherubini}@lirmm.fr.
F. Spindler and F. Chaumette are with INRIA Rennes - Bretagne Atlantique,
IRISA.{firstname.lastname}@inria.fr x d v ! X C R " " . # Y CURRENT IMAGE I KEY IMAGES I1… IN Visual Navigation NEXT KEY IMAGE I d y O x (a) (b)
Fig. 1. General definitions. (a) Top view of the robot (orange), with actuated camera (blue). (b) Current and next key images, and key image database.
is required, the approach is not suitable for our problem. Similarly, [14] uses the robot pose, which is noisy in our framework. Instead, we take inspiration from [15] and [16], where a set of trajectories (arcs of circles) is evaluated for navigating. However, in [15], a sophisticated probabilistic elevation map is used, and the selection of the optimal arc of circle is based on its risk and interest, which both require accurate pose estimation. Similarly, in [16] the candidate trajectories (’tentacles’) are also used for free navigation, which relies on GPS way points, hence - once more - on the robot pose. A deeper comparison with this work is carried out in Sect. IV.
The main contribution of our work is the development of a novel, reactive, pose-independent, tentacle-inspired ob-stacle avoidance technique, which is perfectly suitable for appearance-based tasks, such as visual navigation. The main strengths of this approach are that it is reactive and sensor-based (it does not require any model of the environment), whilst providing useful “look-ahead” information, by ex-ploiting the robot geometric and kinematic characteristics. Our method is experimentally validated in the framework de-signed in [9], and compared with the previous potential field method. In [9], we guaranteed that obstacle avoidance had no effect on the visual task, by discerning two contexts (safe and unsafe), and pursuing the corresponding tasks. Here, the tentacle-based approach intervenes both in assessing the context, and in designing the task in case of danger.
The article is organized as follows. In Sect. II, the control law from [9] is recalled. Then, two alternative obstacle models are presented: vortex potential fields (Sect. III) and tentacles (Sect. IV). Experimental results are reported in Section V, and summarized in the conclusion.
II. CONTROL SCHEME A. General Definitions
The reader is referred to Fig. 1. We define the robot frame FR(R, X, Y ) (R is the robot center of rotation) and image
frameFI(O, x, y) (O is the image center); C is the camera
optical center. The robot control inputs are: u= (v, ω, ˙ϕ) .
These are the translational and angular velocities of the vehicle, and the camera pan angular velocity. We use the normalized perspective camera model, and we assume that the sequence of images that defines the path can be tracked
Fig. 2. Obstacle models with 4 occupied cellsc1, . . . , c4 (purple). (a) Singular cell (blue vectors) and total (red vector) vortex potential fields. (b - e) Tentacles (dashed black), with classification areas (collision in pink, dangerous central in cyan, dangerous external in green), corresponding boxes and delimiting arcs of circle (red, blue and dark green), and cell risk and collision distances (∆ij,δij); ray of cellc1 with respect to the third tentacle,Γ13 (dashed red).
with continuous v (t) > 0. This ensures safety, since only obstacles in front of the robot can be detected by our scanner. The path that the robot must follow is represented as a database of ordered key images, such that successive pairs contain some common static visual features (points). First, the vehicle is manually driven along a taught path, with the camera pointing forward (ϕ = 0), and all the images are saved. Afterwards, a subset (database) ofN key images I1, . . . , IN representing the path (Fig. 1(b)) is selected. Then,
during autonomous navigation, the current image, noted I, is compared with the next key image Id
∈ {I1, . . . , IN},
and a relative pose estimation between I and Id is used
to check when the robot passes the pose where Id was
acquired. For key image selection, and visual point detection and tracking, we use the algorithm in [17]. The output of this algorithm, which is used by our controller, is the set of points visible both inI and Id. Then, navigation consists of driving
the robot forward, while I is driven to Id. We maximize
similarity betweenI and Idusing only the abscissax of the
centroid of the points matched on I and Id. WhenId has been passed, the next image in the set becomes the desired one, and so on, untilIN is reached.
Along with the visual path following problem, we consider obstacles which are on the path, but not in the database, and sensed by the range scanner in a plane parallel to the ground. For obstacle modeling, we use the occupancy grid in Fig. 2(a): it is linked to FR, with cell sides parallel to
X and Y . Its extension is limited (Xm ≤ X ≤ XM and
Ym ≤ Y ≤ YM), to ignore obstacles that are too far to
jeopardize the robot. Any grid cell c centered at (X, Y ) is considered occupied if an obstacle has been sensed in c. For cells entirely lying in the scanner area, only the current scanner reading is considered. For all other cells, we use past readings, which are progressively displaced using odometry. B. Control Design
The desired behaviour of the robot is related to the surrounding obstacles. When the environment is safe, the vehicle should progress forward while remaining near the taught path, with camera pointing forward (ϕ = 0). If avoidable obstacles are present, we apply a robot rotation for circumnavigation with an opposite camera rotation to maintain visibility. Finally, if collision is inevitable, the vehicle should simply stop. To select the behaviour, we assess the danger at time t with a situation risk function H : IR∗+ 7→ [0, 1].
Stability of these tasks has been guaranteed in [9] by: v = (1− H) vs+ Hvu ω = (1− H)λx(xd−x)−jvvs+λϕjϕ˙ϕ jω + Hωu ˙ ϕ = Hλx(xd−x)−jvvu−jωωu jϕ˙ − (1 − H) λϕϕ (1)
In the above equations:
• H ∈ [0, 1] is the situation risk function introduced
above; two alternative definitions, depending on the obstacle model, will be given in Sect. III and IV.
• vs is the translational velocity in the safe context (i.e.,
whenH = 0). It must be reduced when the features are moving quickly in the image, making tracking difficult. This is typically the case at sharp robot turns, and when the camera pan angleϕ is strong. We define vs as:
vs(ω, ϕ) = vm+
vM− vm
4 σ (2)
with functionσ defined as: σ : IR×−π
2, π
2 → [0, 4]
(ω, ϕ)7→ [1+tanh (π−kω|ω|)] [1+tanh (π−kϕ|ϕ|)] .
Function (2) has an upper bound vM > 0 (for ϕ =
ω = 0), and smoothly decreases to the lower bound vm, as either|ϕ| or |ω| grow. The decreasing trend of vs
is determined by empirically tuned positive parameters vM,vm,kω andkϕ. This definition ofvs yields better
results than the one in [9], which was only characterized by the imagex variation.
• vu ∈ [0, vs] is the translational velocity in the unsafe
context (H = 1). It guarantees that the vehicle slows down (and eventually stops) in dangerous situations.
• x and xd are abscissas of the feature centroid
respec-tively in the current and next key image.
• λx> 0 and λϕ> 0 are empirical gains determining the
convergence trend ofx to xd and of ϕ to 0.
• jv, jω and jϕ˙ are the components of the Jacobian
relating ˙x and the control inputs u:
jv= − sin ϕ+x cos ϕζ
jω= RC(cos ϕ+x sin ϕ)ζ + 1 + x2
jϕ˙ = 1 + x2,
with RC and ζ (the centroid depth, hand-tuned ac-cording to the environment characteristics) depicted in Fig. 1(a).
• ωu is the angular velocity that makes the robot avoid
collisions while advancing.
In [9], we proved that (1) is well defined by settingζ > RC/2, and that∀H ∈ [0, 1] obstacle avoidance has no effect on the visual task. Our main contribution here will be in the obstacle model, i.e., in the definition of the variablesH, vu
andωu according to the danger. Two alternative models will
be presented and confronted experimentally. To carry out the comparison, the vortex potentials [9] are briefly recalled in Sect. III. Then, our novel tentacle-based approach is designed and presented in Sect. IV.
III. VORTEX POTENTIAL FIELDS
This approach is illustrated in Fig. 2(a). Given an arbitrary integer K, obstacles are modeled using the latest 2K + 1 scans. For each cell c = (X, Y ), we define the 2K + 1 occupanciesr at the j-th oldest iteration as:
rj(c) ={0, 1}, j = 0, . . . , 2K + 1.
We setrj = 1 if an obstacle has been sensed in c at the j-th
iteration prior to the current one, and0 otherwise. Then, we associate to each cell a coefficient µ (c), obtained by linear combination of the occupancies, weighted with a normalized Gaussian filter that smoothens the cell effect over time:
µ (c) = 2K+1 X j=0 e−(j−K)2/K √ Kπ rj(c) .
The maximum weight is at the K-th latest scan, to avoid overshoot at a new obstacle detection. If the robot velocity is negligible with respect to the scanner frequency, and K is small, the effect of motion on the occupancies can be ignored. In [9], we showed that these assumptions are appropriate in our setup.
The potential associated to each cellc6= R, is defined as: Uc=
µ (c) kck ,
wherekck is the distance from R to c. We define the vortex field for each cell as the rotor ofUc:
fc= f c,X fc,Y = ±∂U∂Yc ∓∂U∂Xc = µ (c) ∓ Y kck3 ± X kck3 .
The signs of fc,X andfc,Y depend onX, so that the field
always points forward, and the fields fc,i generated by all
cells are superimposed to obtain the total field: f =X
i
fc,i.
We then use the magnitude and phase of f (denoted |f| and ∠f ), and two tuned thresholds ∆d and ∆s such that
0 < ∆d < ∆s, to design the situation risk function as:
H= 0 if|f|=0 kf|∠f| if|f |1 ≥∆s 1 if|f |1 ≤∆d 1+kf|∠f | 2 + 1−kf|∠f | 2 tanh ∆d 1−|f |∆d+ ∆s 1−|f |∆s otherwise. Note thatH = 0 if no obstacle is detected, and it is bounded by 1. For small |f|, H is determined by ∠f: the obstacles are far enough to be circumnavigated, and parameter kf ∈
0, 2
π weighs the danger provoked by the field orientation.
Instead, for large|f|, the obstacles are ’too near’, thus H = 1. A hyperbolic function is used to interpolate in between.
In the presence of dangerous obstacles (i.e., for largeH), the robot should slow down, and eventually stop. Imposing v = 0 when H = 1 in (1), yields:
vu= 0.
Hence, in the general case, the first equation in (1) becomes: v = (1− H) vs.
The velocity is reduced fromvsto0, as the risk increases.
To ensure that to circumnavigate the obstacles in danger-ous contexts, the robot aligns its heading with f , we use a gainλf > 0, and set the desired unsafe angular velocity to:
ωu= λf∠f .
IV. TENTACLES
A. Related work
Our new technique is mainly inspired from [16], although some differences, listed below, have been introduced, to deal with the specific constraints of appearance-based navigation. The design in [16], although strengthened by a dynamic analysis, is justified only empirically. For example, the danger of the cells is associated to their orthogonal projection on the arc of circle, without measuring the actual distance to collision. Instead, in the case of two cells with same orthogonal projection (e.g., c1 and c3 in Fig. 2(e)), the
internal cell should be considered more dangerous. Besides, in [16], the requested trajectory is defined by GPS way points. Hence, in the absence of GPS, the approach in [16] becomes purely reactive, while our approach can still follow a path, defined by the image database.
In contrast with that work, our approach does not require a 3D notion of the goal. It must be purely reactive, since the visual task and the obstacle avoidance task are defined in different state spaces (respectively in the image and in the local planar surroundings). As in [16], our grid is built locally at each new scanner acquisition, without accumulating past data, and each tentacle is associated to some classification areas overestimating the vehicle encumbrance. However, these areas are defined and used differently. Their definition is associated to the rigid body kinematics of the boxes representing the vehicle encumbrances, to consider distances to collision. Then, with the largest areas we select the safest tentacle and its risk, and with the thinnest one, the eventual deceleration. Finally, since our vehicle navigates at slightly varying speeds, we do not relate the tentacle sets to v (as in [16]), so that a reduced number of candidate paths is sufficient. Our approach operates locally and instantaneously, without planning nor deriving the robot pose, to determine the values ofH, vu andωu in (1).
B. Classification areas and metrics
We use, along with the set of all occupied grid cells: O = {c1, . . . , cn} ,
a set of drivable paths (tentacles). Each tentaclej is a semi-circle that starts inR, is tangent to X, and is characterized by its curvature (i.e., inverse radius)κj, which belongs toK,
a uniformly sampled set:
κj∈ K = {−κM, . . . , κM} .
The maximum desired curvature κM > 0, must be feasible
considering the robot kinematics. We consider an odd num-ber of tentacles, so that a straight tentacle (withκ = 0) also exists. To illustrate our method, in Fig. 2(b-e), the straight and the sharpest counterclockwise (κ = κM) tentacle are
shown in dashed black. When a total of3 tentacles is used, these correspond respectively toj = 2 and j = 3.
Each tentacle j is characterized by three classification areas (collision, dangerous central, and dangerous external), obtained by rigidly displacing, along the tentacle, three rectangular boxes (red, blue, and dark green in Fig. 2), with increasing width. The boxes, with same height and differ-ent widths, are all overestimated with respect to the robot dimensions, to ensure that, in the presence of disturbances, the actual path is included in the classification area. All three areas are delimited by the box and by three arcs of circle (or lines, in the particular case κ = 0) concentric with the tentacle, and starting from three points (denoted A, B and C) on the box perimeter. In all cases, these points are: the two corners on one side of the box (the outer side must be used ifκ6= 0), and the intersection between the other side (intern ifκ6= 0) and the rear wheel axis. For the collision areas, A, B and C are shown in Fig. 2. We then associate each area to the set of all cells (pink, cyan and light green in Fig. 2) whose center lies within the area. For tentacle j, the three sets of cells are notedCj,Dj andEj. The only exception is
with cells belonging to the dangerous central set, which are not considered in the external set as well:DjT Ej =∅.
During navigation, O is used, along with the sets just defined, to calculate a candidate risk function Hj ∈ [0, 1]
for each tentaclej, and select the best tentacle accordingly. Then, the unsafe translational velocity on the best tentacle, vu, is calculated to adapt the speed to the potential danger,
and to finally deriveωu. All these steps are detailed below.
C. Tentacle risk function
The tentacle risk function Hj is derived from the risk
distance of all occupied cells in the dangerous areas. This distance is denoted∆ij ≥ 0 for each ci∈ OT (DjS Ej).
For occupied cells in the central setDj,∆ijis the distance
that the middle boundary box (blue) would cover along tentacle j before touching the cell center.
For the external set, we consider only the subset ¯Ej ⊆
OT Ej of cells which reduce the clearance in the tentacle
normal direction. For each external occupied cell, we denote Γij the ray starting at the tentacle center and passing through
ci. Cellciis added to ¯Ejif and only if, inDjS Ej, there is at
least an occupied cell crossed byΓij on the other side of the
tentacle. In the example of Fig. 2(e),OT E3={c1, c3, c4},
whereas ¯E3={c1, c3}. Then, for cells in ¯Ej,∆ij is the sum
of two terms: the distance from the center ofcito its normal
projection on the perimeter of the dangerous central area, and the distance that the middle boundary box would cover along tentaclej before reaching the normal projection. The derivation of ∆ij is illustrated, in Fig. 2, for4 cells. Note
that for a given cell,∆ij may have different values (or even
be undefined) according to the tentacle.
When all risk distances on the tentacle are calculated, we compute ∆j as their minimum:
∆j= inf ci∈(O∩Dj)∪ ¯Ej
∆ij.
If (OT Dj)SE¯j ≡ ∅, ∆j =∞. In the example of Fig. 2,
∆2 = ∆12 and ∆3 = ∆33. Obviously, overestimating the
bounding box sizes leads to more conservative∆j.
We then use ∆j and two tuned thresholds ∆d and ∆s
(0 < ∆d < ∆s), to design the tentacle risk function:
Hj= 0 if∆j≥∆s 1 2 h 1 + tanh 1 ∆j−∆d+ 1 ∆j−∆s i if ∆d< ∆j< ∆s 1 if∆j≤∆d. (3) Note that Hj smoothly varies from 0, when the dangerous
cells on the tentacle (if any) are far, to1, when they are near. If Hj = 0, the tentacle is tagged as clear. All the Hjs are
compared (with the strategy explained below), to determine H in (1) and select the best tentacle for navigation. D. Situation risk function and best tentacle
Here we detail our strategy for determining the best tentacle curvatureκb for navigation, and therefore u in (1).
Initially, we calculate the path curvature κ = ω/v ∈ IR that the robot would follow if there were no obstacles. ReplacingH = 0 in (1), it is:
κ =λx xd− x − jvvs+ λϕjϕ˙ϕ /jωvs,
which is always well-defined, since jω 6= 0 and we have
setvs > vm > 0. We obviously constrain κ to the interval
of feasible curvatures[−κM, κM]. Then, we derive the two
neighbors ofκ among all the existing tentacle curvatures: κn, κnn∈ K such that κ ∈ [κn, κnn) .
Letκn be the nearest one, i.e., the curvature of the tentacle
that best approximates the safe path1. We denote it as the
visual task tentacle. The situation risk function Hv of that
tentacle, which measures the risk on the visual path, is obtained by linear interpolation of its neighbours:
Hv=
(Hnn− Hn) κ + Hnκnn− Hnnκn
κnn− κn
. (4) IfHv = 0, the visual task tentacle can be followed: we set
κb = κn, and we apply (1) withH = 0. Instead, if Hv6= 0,
we seek a clear tentacle (Hj = 0). First, to avoid abrupt
control changes, we only search among the tentacles between the visual task one and the best one at the previous iteration2,
notedκpb. If many clear ones are present, the closest to the
visual task tentacle is chosen. If none of the tentacles with curvature in [κn, κpb] is clear, we search among the others.
Again, the best tentacle will be the clear one that is closest toκn and, in case of ambiguity, the one closest toκnn. If
a clear tentacle has been found, we select it and setH = 0. Instead, if no tentacle inK is clear, the one with minimum Hj calculated using (3) is chosen, andH is set equal to that
Hj. Ambiguities are again solved first with the distance from
κn, then fromκnn.
In all cases, the unsafe translational velocityvuis derived
from the obstacles on the best tentacle, as explained below. E. Unsafe translational velocity
The unsafe translational velocity is derived from the colli-sion distance on the best tentacle,δb, which is a conservative
approximation of the maximum distance that the robot can travel along the best tentacle without colliding. Since the thinner (red) box contains the robot, if R follows the best tentacle, collisions can only occur in occupied cells in Cb.
1We consider that intervals are defined even when the first endpoint is
greater than the second:[κn, κnn) must be read (κnn, κn] if κn > κnn. 2At the first iteration, we setκ
In fact, the collision with cell ci will occur at the distance,
denotedδib ≥ 0, that the red box would cover along the best
tentacle, before touching the center ofci. The derivation of
δib is illustrated in Fig. 2 for four occupied cells.
Then, we define δb as the minimum among the collision
distances of all occupied cells in Cb:
δb= inf
ci∈O∩Cb
δib.
If all cells inCb are free,δb =∞. In the example of Fig. 2,
assuming the best tentacle is the straight one (b = 2), δb =
δ12. Again, oversizing the box leads to more conservativeδb.
The translational velocity must be designed accord-ingly. Let δd and δs be two tuned thresholds such that
0 < δd < δs. If the probable collision is far enough
(δb ≥ δs), v can be maintained at the safe value defined
in (2). Instead, if it is near (δb≤ δd), the robot should stop.
To comply with the boundary conditions vu(δd) = 0 and
vu(δs) = vs, in between we apply a constant deceleration:
a = vs2/2(δd− δs) < 0.
Since the distance required for braking at velocityvu(δb) is:
δb− δd=−v2u/2a,
the expression of the unsafe translational velocity becomes:
vu(δb) = vs ifδb ≥ δs vspδb− δd/δs− δd ifδd < δb< δs 0 ifδb ≤ δd, (5)
in order to decelerate as the collision distance decreases. F. Unsafe angular velocity
Once the best tentacle (with curvatureκb) is chosen, and
the correspondingvu is obtained with (5), we set:
ωu= vuκb. (6)
Setting this value of unsafe angular velocity in (1) guarantees that when H = 1, the robot precisely follows the best tentacle, with translational velocity vu.
G. Discussion
The values of H, vu andωu derived as explained above
are inserted in (1) to derive the control inputs u.
WhenH = 0, the robot tracks at its best the taught path: the image error is regulated by ω, while v is set to vs to
improve tracking, and the camera is driven forward (ϕ = 0). This occurs if the2 neighbour tentacles are clear, while in the vortex approach, even a single occupied cell would generate H > 0. Thus, one advantage of the new approach is that only obstacles on the visual path are taken into account. When H = 1, ˙ϕ ensures the visual task, and the two other inputs guarantee that the best tentacle is followed:ω/v = κb. The
applied curvature fluctuates less than with the potential fields, where it is driven by strongly varying f .
In general, the robot navigates between the taught path, and the best path considering obstacles. Only the transition, but not the speed, is driven by H. In fact, note that, for all H ∈ [0, 1], when δb ≥ δs: v = vs. This is another
advantage of tentacles: a high velocity can be applied if the path is clear up to δs. With vortex fields, instead, the
vehicle stops frequently (as soon as H = 1). Finally, one may object that processing can be costly. However, since ∆ij andδij are invariant geometric characteristics related to
the cell positions, their values at each cell can be computed and stored offline, for use when the cell becomes occupied.
5 m 5 m 5 m 5 m barrier barrier llarge 2 obstacles obstacle 2 obstacles obstacle A 2 A 1 A.2 A.1
Fig. 3. Two obstacle scenarios with taught (white) and replayed (red: using tentacles, black: using potentials) paths.
Fig. 4. Control inputs using tentacles in scenario A.1 (top) and A.2
(bottom):v (black, in ms−1),ω (green, in rads−1), andϕ (red, in rads˙ −1).
The iterations with strongH are highlighted in yellow.
V. EXPERIMENTS
Here, we report the experiments (also shown in the video attached to this paper) that we performed to validate our approach. All experiments have been carried out on our CyCab robot, equipped with a 70◦ field of view, B&W
Marlin (F-131B) camera mounted on a TRACLabs Biclops Pan/Tilt head, and with a 2-layer, 110◦ scanning angle,
laser SICK LD-MRS. The grid is built by projecting the readings from the 2 layers on the ground, and by using: XM = YM = 10 m, Xm=−2 m, Ym=−10 m. The cells
have size20× 20 cm. We use 21 tentacles, with κM = 0.35
m−1 (the Cycab maximum applicable curvature).
First, we have compared the two obstacle avoidance meth-ods (vortex potential fields and tentacles) in the experiments in Fig. 3. The taught path (denoted A, and white in the figure) is 60 m long. By placing various obstacles, we design the scenarios A.1 (with a long obstacle perpendicular to the path) and A.2 (with two avoidable obstacles and a blocking barrier). Then, we attempt to replay path A in each scenario, using either technique. The replayed paths, estimated from odometry and snapshots, are drawn in black (potentials) and red (tentacles). The control inputs u using tentacles are plotted in Fig. 4, with dangerous iterations (i.e., with strong H) highlighted in yellow. The smooth trend of u at the beginning and end is due to the acceleration saturation carried out by the CyCab low-level control. In Fig. 5, we have plotted the curvaturesω/v that are applied in the 4 experiments. Since our preliminary tests, it was clear that tentacles could be implemented at higher speeds than potentials, since they provide look-ahead information, and a stabler model. Hence, in (2), we set: vM = 1 ms−1 with
tentacles,vM = 0.4 with potentials, and vm= 0.3 for both.
ForvM > 0.4, potentials fail to avoid the obstacles, while
with tentacles, the velocity has been limited to reduce the motion of features between successive images; the maximum speed attainable by the CyCab is1.3 ms−1 anyway.
In scenario A.1, the long obstacle cannot be circum-navigated using potentials. It induces oscillations on the orientation∠f , hence on the applied curvature (solid black curve in Fig. 5), until the robot is too near to the obstacle, and eventually stops. Instead, using tentacles, the obstacle is overtaken on the left, while the camera rotates right to maintain scene visibility (green and red curves in Fig. 4, top). The robot successfully reaches the final key image and completes navigation, although it is driven over 5 meters away from the taught path. In practice, soon after the obstacle
0.4 0.4 15 60 15 4545 6060 distance covered (m) 0 4 distance covered (m) -0.40.4
Fig. 5. Applied curvatureω/v (in m−1) in scenario A.1 (solid) and A.2
(dashed) using tentacles (red) and potentials (black).
Fig. 6. Map of the four navigation paths B, C, D, E (a), and validation
with: irrelevant obstacles (b), traffic (c) and a moving pedestrian (d). The visual task tentacle is shown in red, and the best tentacle (when different) in blue; only cells that can activateH (i.e., cells at distance ∆ < ∆s) have
been drawn, with brightness proportional to∆.
is detected, tentacles with first positive (5− 16 s), and then negative (16 − 25 s) curvatures are selected. Since these tentacles are clear, v is reduced only for visual tracking, by (2) (black curve in Fig. 4, top). This is an advantage over the too conservative potential fields, which do not consider the real collision risk, and force the stop. After 25 s, the environment returns clear (H = 0), so the visual tentacle can be followed again, and the robot is driven back to the path. Then (38− 52 s) a small bush on the left triggers H and causes a rotation along with a slight decrease in v. Then the context returns safe, and the visual path can be followed until the end. The translational velocity averaged over the experiment is0.79 ms−1, which is more than twice
the speed reached in [9].
In scenario A.2, with both methods Cycab navigates without colliding and stops at the barrier. However, as aforementioned, the average navigation velocitiesv are very different, i.e.,0.83 ms−1with tentacles, and only0.35 ms−1
with potentials. Moreover, the applied curvature varies less in the first case (see dashed curves in Fig. 5). This leads to smoother and faster navigation than with potentials. When the barrier is reached, the vortex method behaves as in A.1 to force the stop. Instead, the new method seeks a feasible path until all tentacles are occupied. Then, (5) makesv gradually decrease to zero (black curve in Fig. 4, bottom).
After these results, which confirmed the advantages of the new over the old method, we have run some experiments, uniquely with tentacles, on longer and more crowded paths, shown in Fig. 6(a). The Cycab completed all paths (including 650 m long path E), while dealing with various natural and unpredictable obstacles, such as parked and driving cars, pedestrians, and even bicycles. A first result that emerged from the experiments was that, by assessing the collision risk only along the visual path, non-dangerous obstacles (e.g., walls or cars parked on the sides) are not taken into account. This is clear from Fig. 6(b): the cars parked on the right (which were not present during teaching) do not belong to any of the visual task tentacle classification areas. Hence, they are irrelevant, and do not deviate the robot from the path. Another nice behavior is shown in Fig. 6(c): if a stationing car is unavoidable, the robot decelerates and stops with (5), but, as soon as the car departs, it gradually accelerates
(again with (5)), to resume navigation. An experiment with a crossing pedestrian is presented in Fig. 6(d). The pedestrian is considered irrelevant, until it enters the visual task tentacle. Then, the clockwise tentacles (blue in the figure) are selected to pass between the person and the right sidewalk. When the path is clear again, the robot turns left to recover it.
VI. CONCLUSIONS
We have presented a novel, robust and reactive technique for avoiding obstacles with a wheeled robot. By exploiting the robot kinematics, we can predict collisions at look-ahead distances along candidate circular paths (tentacles). Since our method is sensor-based and pose-independent, it is perfectly suited for visual navigation. Extensive experiments show that it generates smoother control inputs than its predecessor, and that it can be applied in realistic situations. To our knowl-edge, this is the first time that outdoor visual navigation with obstacle avoidance is carried out at approximately 1 ms−1
on over 500 m, using neither GPS nor maps. Perspective work includes using a more sophisticated obstacle model (e.g., with shape, dimension and velocity), to design an optimal/complete rather than a worst case algorithm.
ACKNOWLEDGMENT
This work has been supported by ANR (French National Agency) CityVIP project under grant ANR-07 TSFA-013-01.
REFERENCES
[1] U. Nunes, C. Laugier and M. Trivedi, “Introducing perception, plan-ning, and navigation for Intelligent Vehicles” in IEEE Trans. on Intelligent Transportation Systems, vol. 10, no. 3, 2009, pp. 375–379. [2] M. Buehler, K. Lagnemma and S. Singh (Editors), “Special Issue on the 2007 DARPA Urban Challenge, Part I-III”, in Journal of Field Robotics, vol. 25, no. 8–10, 2008, pp. 423–860.
[3] T. Wada, S. Doi and S. Hiraoka, “A deceleration control method of automobile for collision avoidance based on driver’s perceptual risk”, IROS, 2009.
[4] T. Kato, Y. Ninomiya and I. Masaki, “An obstacle detection method by fusion of radar and motion stereo”, in IEEE Trans. on Intelligent Transportation Systems, vol. 3, no. 3, 2002, pp. 182–188.
[5] A. Ohya, A. Kosaka and A. Kak, “Vision-based navigation by a mobile robot with obstacle avoidance using a single-camera vision and ultrasonic sensing”, IEEE Trans. on Robotics and Automation, vol. 14, no. 6, 1998, pp. 969–978.
[6] Z. Yan, X. Xiaodong, P. Xuejun and W. Wei, “Mobile robot indoor navigation using laser range finder and monocular vision”, IEEE Int. Conf. on Robotics, Intelligent Systems and Signal Processing, 2003. [7] F. Lamiraux, D. Bonnafous and O. Lefebvre, “Reactive path
deforma-tion for nonholonomic mobile robots”, in IEEE Trans. on Robotics, vol. 20, no. 6, 2004, pp. 967–977.
[8] T.-S. Lee, G.-H. Eoh, J. Kim and B.-H. Lee, “Mobile robot navigation with reactive free space estimation”, IROS, 2010.
[9] A. Cherubini and F. Chaumette, “Visual navigation with obstacle avoidance”, IROS, 2011.
[10] O. Khatib, “Real-time obstacle avoidance for manipulators and mobile robots”, ICRA, 1985.
[11] J. Borenstein and Y. Koren, “The Vector Field Histogram - Fast obstacle avoidance for mobile robots”, IEEE Trans. on Robotics and Automation, vol. 7, no. 3, 1991, pp. 278-288.
[12] D. Fox, W. Burgard and S. Thrun, “The Dynamic Window approach to obstacle avoidance”, IEEE Robotics and Automation Magazine, vol. 4, no. 1, 1997, pp. 23–33.
[13] J. Minguez, “The Obstacle-Restriction Method (ORM) for robot obstacle avoidance in difficult environments”, IROS, 2005.
[14] M. Mujahad, D. Fischer, B. Mertsching and H. Jaddu “Closest Gap based (CG) reactive obstacle avoidance navigation for highly cluttered environments”, IROS, 2010.
[15] D. Bonnafous, S. Lacroix and T. Sim´eon, “Motion generation for a rover on rough terrains”, IROS, 2001.
[16] F. von Hundelshausen, M. Himmelsbach, F. Hecker, A. Mueller and H.-J. Wuensche, “Driving with tentacles-Integral structures of sensing and motion”, in Journal of Field Robotics, vol. 25, no. 9, 2008, pp. 640–673.
[17] E. Royer, M. Lhuillier, M. Dhome and J.-M. Lavest, “Monocular vision for mobile robot localization and autonomous navigation”, Int. Journal of Computer Vision, vol. 74, no. 3, 2007, pp. 237–260.
